This file serves to be a supplementary document that describes all the statistics results performed for this project. It may help to test some new questions that are not included in the corresponding slides.
This file displays the results of the FaceWord project (data collected at NYU). There are two experiments in this project. In Experiment 1, Chinese participants viewed Chinese faces and characters in four conditions (Layout: intact, exchange [top and bottom parts were switched], top and bottom) and completed an additional localizer (Chinese faces, Chinese characters, objects, scrambled objects). In Experiment 2, English speakers viewed Chinese characters and English words in four conditions (Layout: intact, exchange, top [top parts of Chinese characters; left two letters for English words] and bottom [bottom parts of Chinese characters; right four letters for English words]) and completed an additional localizer (Caucasian faces, English words, objects, scrambled objects).
For the main runs, analysis is conducted for each ROI separately (FFA1, FFA2, VWFA, LOC).
For each ROI, three analyses are performed:
libsvm is used to decode different condition pairs (see below) and one-tail one-sample t-tests is used to test if the pair of conditions can be decoded [whether the accuracy is significantly larger than the chancel level (0.5); one-tail one-sample t-tests].
The probability was estimated for each particiapnt separately:
libsvm) is trained with the patterns of intact vs. exchange (10 runs).The above table displays the size (in mm2) of each label for each participant. (NA denotes that this label is not available for that particiapnt.)
The above table displays the number of vertices for each label and each participant. (NA denotes that this label is not available for that particiapnt.)
The above table dispalys the number of participants included in the following analyses for each ROI. (VWFA is only found on the left hemisphere.)
## Anova Table (Type 3 tests)
##
## Response: Response
## Effect df MSE F ges p.value
## 1 FaceWord 1, 11 0.19 9.30 * .13 .01
## 2 Layout 2.33, 25.60 0.03 10.14 *** .05 .0003
## 3 FaceWord:Layout 2.41, 26.50 0.02 2.52 + .01 .09
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
##
## Sphericity correction method: GG
Posthoc analysis for the main effects:
## contrast estimate SE df t.ratio p.value
## faces - words 0.271 0.0888 11 3.050 0.0111
##
## Results are averaged over the levels of: Layout
## contrast estimate SE df t.ratio p.value
## intact - exchange 0.0741 0.0416 33 1.781 0.3002
## intact - top 0.2140 0.0416 33 5.141 0.0001
## intact - bottom 0.1566 0.0416 33 3.761 0.0035
## exchange - top 0.1398 0.0416 33 3.359 0.0102
## exchange - bottom 0.0824 0.0416 33 1.980 0.2159
## top - bottom -0.0574 0.0416 33 -1.379 0.5209
##
## Results are averaged over the levels of: FaceWord
## P value adjustment: tukey method for comparing a family of 4 estimates
Results of simple effect analysis (uncorrected):
## Layout FaceWord contrast estimate SE df t.ratio p.value
## intact . faces - words 0.34161 0.1009 17.8 3.387 0.0033
## exchange . faces - words 0.21131 0.1009 17.8 2.095 0.0507
## top . faces - words 0.35013 0.1009 17.8 3.471 0.0028
## bottom . faces - words 0.18019 0.1009 17.8 1.786 0.0911
## . faces intact - exchange 0.13929 0.0571 65.7 2.440 0.0174
## . faces intact - top 0.20971 0.0571 65.7 3.674 0.0005
## . faces intact - bottom 0.23728 0.0571 65.7 4.157 0.0001
## . faces exchange - top 0.07042 0.0571 65.7 1.234 0.2217
## . faces exchange - bottom 0.09798 0.0571 65.7 1.716 0.0908
## . faces top - bottom 0.02756 0.0571 65.7 0.483 0.6308
## . words intact - exchange 0.00899 0.0571 65.7 0.157 0.8754
## . words intact - top 0.21823 0.0571 65.7 3.823 0.0003
## . words intact - bottom 0.07586 0.0571 65.7 1.329 0.1885
## . words exchange - top 0.20924 0.0571 65.7 3.665 0.0005
## . words exchange - bottom 0.06687 0.0571 65.7 1.171 0.2457
## . words top - bottom -0.14238 0.0571 65.7 -2.494 0.0152
## Anova Table (Type 3 tests)
##
## Response: Response
## Effect df MSE F ges p.value
## 1 FaceWord 1, 16 0.34 25.86 *** .20 .0001
## 2 Layout 2.56, 40.95 0.06 4.41 * .02 .01
## 3 FaceWord:Layout 2.52, 40.29 0.06 4.63 * .02 .01
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
##
## Sphericity correction method: GG
Posthoc analysis for the main effects:
## contrast estimate SE df t.ratio p.value
## faces - words 0.505 0.0994 16 5.085 0.0001
##
## Results are averaged over the levels of: Layout
## contrast estimate SE df t.ratio p.value
## intact - exchange 0.15731 0.0536 48 2.933 0.0255
## intact - top 0.16926 0.0536 48 3.156 0.0142
## intact - bottom 0.14869 0.0536 48 2.773 0.0382
## exchange - top 0.01195 0.0536 48 0.223 0.9960
## exchange - bottom -0.00861 0.0536 48 -0.161 0.9985
## top - bottom -0.02057 0.0536 48 -0.383 0.9806
##
## Results are averaged over the levels of: FaceWord
## P value adjustment: tukey method for comparing a family of 4 estimates
Results of simple effect analysis (uncorrected):
## Layout FaceWord contrast estimate SE df t.ratio p.value
## intact . faces - words 0.74207 0.1182 30.3 6.279 <.0001
## exchange . faces - words 0.40872 0.1182 30.3 3.458 0.0016
## top . faces - words 0.41798 0.1182 30.3 3.537 0.0013
## bottom . faces - words 0.45219 0.1182 30.3 3.826 0.0006
## . faces intact - exchange 0.32398 0.0749 95.9 4.327 <.0001
## . faces intact - top 0.33130 0.0749 95.9 4.425 <.0001
## . faces intact - bottom 0.29363 0.0749 95.9 3.922 0.0002
## . faces exchange - top 0.00732 0.0749 95.9 0.098 0.9223
## . faces exchange - bottom -0.03035 0.0749 95.9 -0.405 0.6861
## . faces top - bottom -0.03767 0.0749 95.9 -0.503 0.6160
## . words intact - exchange -0.00937 0.0749 95.9 -0.125 0.9007
## . words intact - top 0.00722 0.0749 95.9 0.096 0.9234
## . words intact - bottom 0.00375 0.0749 95.9 0.050 0.9601
## . words exchange - top 0.01658 0.0749 95.9 0.222 0.8252
## . words exchange - bottom 0.01312 0.0749 95.9 0.175 0.8612
## . words top - bottom -0.00346 0.0749 95.9 -0.046 0.9632
The above figure shows the neural respones (beta values) in FFA1 for each condition. The numbers are the p-values for the tests of differences between intact vs. exchange in that condition. Error bars represent 95% confidence intervals. Note: , p < .05; **, p <.001
The above figure shows the decoding accuracy in FFA1 for each pair. The numbers are the p-values for the one-tail one-sample t-tests against the chance level (0.5) in that condition. Error bars represent 95% confidence intervals. Note: , p < .05; , p < .01; , p <.001
The above figure shows the probability of top+bottom being decoded as exchange conditions in FFA1. Patterns of top and bottom were combined with different weights, i.e., “face_top0.25-face_bottom0.75” denotes the linear combinations of face_top and face_bottom with the weights of 0.25/0.75. The numbers are the p-values for the two-tail one-sample t-tests against the chance level (0.5) in that condition. Error bars represent 95% confidence intervals.
## Anova Table (Type 3 tests)
##
## Response: Response
## Effect df MSE F ges p.value
## 1 FaceWord 1, 13 0.07 1.50 .006 .24
## 2 Layout 2.52, 32.76 0.02 10.40 *** .03 .0001
## 3 FaceWord:Layout 2.46, 31.96 0.03 0.44 .002 .69
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
##
## Sphericity correction method: GG
Posthoc analysis for the main effects:
## contrast estimate SE df t.ratio p.value
## faces - words 0.0606 0.0494 13 1.226 0.2419
##
## Results are averaged over the levels of: Layout
## contrast estimate SE df t.ratio p.value
## intact - exchange 0.1112 0.0338 39 3.291 0.0110
## intact - top 0.1868 0.0338 39 5.526 <.0001
## intact - bottom 0.0842 0.0338 39 2.493 0.0769
## exchange - top 0.0755 0.0338 39 2.235 0.1318
## exchange - bottom -0.0270 0.0338 39 -0.798 0.8548
## top - bottom -0.1025 0.0338 39 -3.033 0.0214
##
## Results are averaged over the levels of: FaceWord
## P value adjustment: tukey method for comparing a family of 4 estimates
Results of simple effect analysis (uncorrected):
## Layout FaceWord contrast estimate SE df t.ratio p.value
## intact . faces - words 0.11378 0.0720 41.2 1.581 0.1216
## exchange . faces - words 0.05975 0.0720 41.2 0.830 0.4113
## top . faces - words 0.05176 0.0720 41.2 0.719 0.4761
## bottom . faces - words 0.01708 0.0720 41.2 0.237 0.8137
## . faces intact - exchange 0.13824 0.0545 74.1 2.537 0.0133
## . faces intact - top 0.21776 0.0545 74.1 3.997 0.0002
## . faces intact - bottom 0.13260 0.0545 74.1 2.434 0.0174
## . faces exchange - top 0.07952 0.0545 74.1 1.460 0.1486
## . faces exchange - bottom -0.00564 0.0545 74.1 -0.104 0.9178
## . faces top - bottom -0.08516 0.0545 74.1 -1.563 0.1223
## . words intact - exchange 0.08420 0.0545 74.1 1.546 0.1265
## . words intact - top 0.15574 0.0545 74.1 2.858 0.0055
## . words intact - bottom 0.03589 0.0545 74.1 0.659 0.5121
## . words exchange - top 0.07153 0.0545 74.1 1.313 0.1932
## . words exchange - bottom -0.04832 0.0545 74.1 -0.887 0.3780
## . words top - bottom -0.11985 0.0545 74.1 -2.200 0.0309
## Anova Table (Type 3 tests)
##
## Response: Response
## Effect df MSE F ges p.value
## 1 FaceWord 1, 14 0.17 19.27 *** .14 .0006
## 2 Layout 2.47, 34.55 0.02 10.20 *** .03 .0001
## 3 FaceWord:Layout 1.96, 27.47 0.04 3.89 * .01 .03
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
##
## Sphericity correction method: GG
Posthoc analysis for the main effects:
## contrast estimate SE df t.ratio p.value
## faces - words 0.327 0.0746 14 4.390 0.0006
##
## Results are averaged over the levels of: Layout
## contrast estimate SE df t.ratio p.value
## intact - exchange 0.1897 0.0366 42 5.179 <.0001
## intact - top 0.1549 0.0366 42 4.230 0.0007
## intact - bottom 0.1016 0.0366 42 2.775 0.0395
## exchange - top -0.0347 0.0366 42 -0.948 0.7791
## exchange - bottom -0.0880 0.0366 42 -2.404 0.0919
## top - bottom -0.0533 0.0366 42 -1.456 0.4728
##
## Results are averaged over the levels of: FaceWord
## P value adjustment: tukey method for comparing a family of 4 estimates
Results of simple effect analysis (uncorrected):
## Layout FaceWord contrast estimate SE df t.ratio p.value
## intact . faces - words 0.49653 0.0899 27.7 5.523 <.0001
## exchange . faces - words 0.24478 0.0899 27.7 2.723 0.0111
## top . faces - words 0.28897 0.0899 27.7 3.214 0.0033
## bottom . faces - words 0.27898 0.0899 27.7 3.103 0.0044
## . faces intact - exchange 0.31555 0.0550 82.9 5.737 <.0001
## . faces intact - top 0.25873 0.0550 82.9 4.704 <.0001
## . faces intact - bottom 0.21040 0.0550 82.9 3.826 0.0003
## . faces exchange - top -0.05682 0.0550 82.9 -1.033 0.3045
## . faces exchange - bottom -0.10515 0.0550 82.9 -1.912 0.0594
## . faces top - bottom -0.04832 0.0550 82.9 -0.879 0.3821
## . words intact - exchange 0.06380 0.0550 82.9 1.160 0.2494
## . words intact - top 0.05116 0.0550 82.9 0.930 0.3550
## . words intact - bottom -0.00715 0.0550 82.9 -0.130 0.8969
## . words exchange - top -0.01264 0.0550 82.9 -0.230 0.8189
## . words exchange - bottom -0.07094 0.0550 82.9 -1.290 0.2007
## . words top - bottom -0.05831 0.0550 82.9 -1.060 0.2921
The above figure shows the neural respones (beta values) in FFA2 for each condition. The numbers are the p-values for the tests of differences between intact vs. exchange in that condition. Error bars represent 95% confidence intervals. Note: , p < .05; **, p <.001
The above figure shows the decoding accuracy in FFA2 for each pair. The numbers are the p-values for the one-tail one-sample t-tests against the chance level (0.5) in that condition. Error bars represent 95% confidence intervals. Note: , p < .05; **, p <.001
The above figure shows the probability of top+bottom being decoded as exchange conditions in FFA2. Patterns of top and bottom were combined with different weights, i.e., “face_top0.25-face_bottom0.75” denotes the linear combinations of face_top and face_bottom with the weights of 0.25/0.75. The numbers are the p-values for the two-tail one-sample t-tests against the chance level (0.5) in that condition. Error bars represent 95% confidence intervals.
## Anova Table (Type 3 tests)
##
## Response: Response
## Effect df MSE F ges p.value
## 1 FaceWord 1, 16 0.16 59.65 *** .13 <.0001
## 2 Layout 2.50, 39.98 0.03 2.93 + .004 .05
## 3 FaceWord:Layout 2.49, 39.82 0.02 8.46 *** .008 .0004
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
##
## Sphericity correction method: GG
Posthoc analysis for the main effects:
## contrast estimate SE df t.ratio p.value
## faces - words -0.538 0.0696 16 -7.724 <.0001
##
## Results are averaged over the levels of: Layout
## contrast estimate SE df t.ratio p.value
## intact - exchange -0.01212 0.0403 48 -0.301 0.9904
## intact - top 0.09355 0.0403 48 2.321 0.1075
## intact - bottom 0.00265 0.0403 48 0.066 0.9999
## exchange - top 0.10567 0.0403 48 2.622 0.0549
## exchange - bottom 0.01477 0.0403 48 0.366 0.9830
## top - bottom -0.09090 0.0403 48 -2.255 0.1232
##
## Results are averaged over the levels of: FaceWord
## P value adjustment: tukey method for comparing a family of 4 estimates
Results of simple effect analysis (uncorrected):
## Layout FaceWord contrast estimate SE df t.ratio p.value
## intact . faces - words -0.44403 0.0812 28.4 -5.468 <.0001
## exchange . faces - words -0.67875 0.0812 28.4 -8.358 <.0001
## top . faces - words -0.39309 0.0812 28.4 -4.841 <.0001
## bottom . faces - words -0.63536 0.0812 28.4 -7.824 <.0001
## . faces intact - exchange 0.10524 0.0528 93.5 1.993 0.0492
## . faces intact - top 0.06808 0.0528 93.5 1.289 0.2005
## . faces intact - bottom 0.09831 0.0528 93.5 1.862 0.0658
## . faces exchange - top -0.03716 0.0528 93.5 -0.704 0.4834
## . faces exchange - bottom -0.00692 0.0528 93.5 -0.131 0.8960
## . faces top - bottom 0.03023 0.0528 93.5 0.573 0.5684
## . words intact - exchange -0.12949 0.0528 93.5 -2.452 0.0161
## . words intact - top 0.11902 0.0528 93.5 2.254 0.0266
## . words intact - bottom -0.09302 0.0528 93.5 -1.761 0.0814
## . words exchange - top 0.24850 0.0528 93.5 4.706 <.0001
## . words exchange - bottom 0.03647 0.0528 93.5 0.691 0.4916
## . words top - bottom -0.21204 0.0528 93.5 -4.015 0.0001
The above figure shows the neural respones (beta values) in VWFA for each condition. The numbers are the p-values for the tests of differences between intact vs. exchange in that condition. Error bars represent 95% confidence intervals. Note: *, p < .05
The above figure shows the decoding accuracy in VWFA for each pair. The numbers are the p-values for the one-tail one-sample t-tests against the chance level (0.5) in that condition. Error bars represent 95% confidence intervals. Note: ***, p <.001
The above figure shows the probability of top+bottom being decoded as exchange conditions in VWFA. Patterns of top and bottom were combined with different weights, i.e., “face_top0.25-face_bottom0.75” denotes the linear combinations of face_top and face_bottom with the weights of 0.25/0.75. The numbers are the p-values for the two-tail one-sample t-tests against the chance level (0.5) in that condition. Error bars represent 95% confidence intervals.
## Anova Table (Type 3 tests)
##
## Response: Response
## Effect df MSE F ges p.value
## 1 FaceWord 1, 17 0.45 12.63 ** .03 .002
## 2 Layout 1.78, 30.24 0.09 0.51 .0004 .58
## 3 FaceWord:Layout 2.63, 44.64 0.04 1.05 .0006 .37
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
##
## Sphericity correction method: GG
Posthoc analysis for the main effects:
## contrast estimate SE df t.ratio p.value
## faces - words -0.399 0.112 17 -3.554 0.0024
##
## Results are averaged over the levels of: Layout
## contrast estimate SE df t.ratio p.value
## intact - exchange 0.00832 0.0529 51 0.157 0.9986
## intact - top 0.06032 0.0529 51 1.139 0.6672
## intact - bottom 0.02557 0.0529 51 0.483 0.9626
## exchange - top 0.05200 0.0529 51 0.982 0.7602
## exchange - bottom 0.01725 0.0529 51 0.326 0.9879
## top - bottom -0.03475 0.0529 51 -0.656 0.9128
##
## Results are averaged over the levels of: FaceWord
## P value adjustment: tukey method for comparing a family of 4 estimates
Results of simple effect analysis (uncorrected):
## Layout FaceWord contrast estimate SE df t.ratio p.value
## intact . faces - words -0.35647 0.1238 24.7 -2.878 0.0081
## exchange . faces - words -0.45834 0.1238 24.7 -3.701 0.0011
## top . faces - words -0.33688 0.1238 24.7 -2.720 0.0118
## bottom . faces - words -0.44556 0.1238 24.7 -3.598 0.0014
## . faces intact - exchange 0.05925 0.0679 97.5 0.873 0.3851
## . faces intact - top 0.05053 0.0679 97.5 0.744 0.4586
## . faces intact - bottom 0.07011 0.0679 97.5 1.032 0.3044
## . faces exchange - top -0.00872 0.0679 97.5 -0.128 0.8980
## . faces exchange - bottom 0.01086 0.0679 97.5 0.160 0.8733
## . faces top - bottom 0.01958 0.0679 97.5 0.288 0.7736
## . words intact - exchange -0.04262 0.0679 97.5 -0.628 0.5317
## . words intact - top 0.07012 0.0679 97.5 1.033 0.3044
## . words intact - bottom -0.01897 0.0679 97.5 -0.279 0.7805
## . words exchange - top 0.11273 0.0679 97.5 1.660 0.1001
## . words exchange - bottom 0.02364 0.0679 97.5 0.348 0.7285
## . words top - bottom -0.08909 0.0679 97.5 -1.312 0.1926
## Anova Table (Type 3 tests)
##
## Response: Response
## Effect df MSE F ges p.value
## 1 FaceWord 1, 18 0.15 7.85 * .010 .01
## 2 Layout 2.37, 42.59 0.05 4.51 * .004 .01
## 3 FaceWord:Layout 2.54, 45.67 0.04 0.99 .0008 .40
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
##
## Sphericity correction method: GG
Posthoc analysis for the main effects:
## contrast estimate SE df t.ratio p.value
## faces - words -0.176 0.0628 18 -2.802 0.0118
##
## Results are averaged over the levels of: Layout
## contrast estimate SE df t.ratio p.value
## intact - exchange 0.0912 0.0454 54 2.010 0.1971
## intact - top 0.1576 0.0454 54 3.474 0.0055
## intact - bottom 0.0395 0.0454 54 0.871 0.8198
## exchange - top 0.0664 0.0454 54 1.464 0.4660
## exchange - bottom -0.0517 0.0454 54 -1.139 0.6672
## top - bottom -0.1181 0.0454 54 -2.603 0.0560
##
## Results are averaged over the levels of: FaceWord
## P value adjustment: tukey method for comparing a family of 4 estimates
Results of simple effect analysis (uncorrected):
## Layout FaceWord contrast estimate SE df t.ratio p.value
## intact . faces - words -0.0867 0.0814 44.1 -1.064 0.2929
## exchange . faces - words -0.2075 0.0814 44.1 -2.548 0.0144
## top . faces - words -0.2077 0.0814 44.1 -2.550 0.0143
## bottom . faces - words -0.2018 0.0814 44.1 -2.479 0.0171
## . faces intact - exchange 0.1516 0.0620 107.5 2.443 0.0162
## . faces intact - top 0.2181 0.0620 107.5 3.514 0.0006
## . faces intact - bottom 0.0971 0.0620 107.5 1.565 0.1206
## . faces exchange - top 0.0665 0.0620 107.5 1.071 0.2864
## . faces exchange - bottom -0.0545 0.0620 107.5 -0.878 0.3817
## . faces top - bottom -0.1210 0.0620 107.5 -1.950 0.0538
## . words intact - exchange 0.0307 0.0620 107.5 0.496 0.6213
## . words intact - top 0.0971 0.0620 107.5 1.564 0.1207
## . words intact - bottom -0.0181 0.0620 107.5 -0.291 0.7712
## . words exchange - top 0.0663 0.0620 107.5 1.069 0.2875
## . words exchange - bottom -0.0488 0.0620 107.5 -0.787 0.4330
## . words top - bottom -0.1152 0.0620 107.5 -1.856 0.0662
The above figure shows the neural respones (beta values) in LO for each condition. The numbers are the p-values for the tests of differences between intact vs. exchange in that condition. Error bars represent 95% confidence intervals. Note: *, p < .05
The above figure shows the decoding accuracy in LO for each pair. The numbers are the p-values for the one-tail one-sample t-tests against the chance level (0.5) in that condition. Error bars represent 95% confidence intervals. Note: , p < .01; *, p <.001
The above figure shows the probability of top+bottom being decoded as exchange conditions in LO. Patterns of top and bottom were combined with different weights, i.e., “face_top0.25-face_bottom0.75” denotes the linear combinations of face_top and face_bottom with the weights of 0.25/0.75. The numbers are the p-values for the two-tail one-sample t-tests against the chance level (0.5) in that condition. Error bars represent 95% confidence intervals.
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Mojave 10.14.5
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] tools stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] ggpubr_0.2.5 magrittr_1.5 emmeans_1.4.2 lmerTest_3.1-0 afex_0.25-1 lme4_1.1-21 Matrix_1.2-18 forcats_0.4.0 stringr_1.4.0 dplyr_0.8.5 purrr_0.3.3 readr_1.3.1 tidyr_1.0.2 tibble_2.1.3 ggplot2_3.3.0 tidyverse_1.2.1
##
## loaded via a namespace (and not attached):
## [1] httr_1.4.1 jsonlite_1.6.1 splines_3.6.3 carData_3.0-3 modelr_0.1.5 assertthat_0.2.1 cellranger_1.1.0 yaml_2.2.1 numDeriv_2016.8-1.1 pillar_1.4.3 backports_1.1.5 lattice_0.20-38 glue_1.3.2 digest_0.6.25 ggsignif_0.6.0 rvest_0.3.5 minqa_1.2.4 colorspace_1.4-1 cowplot_1.0.0 htmltools_0.4.0 plyr_1.8.6 pkgconfig_2.0.3
## [23] broom_0.5.3.9000 haven_2.2.0 xtable_1.8-4 mvtnorm_1.0-11 scales_1.0.0 openxlsx_4.1.3 rio_0.5.16 generics_0.0.2 car_3.0-5 ellipsis_0.3.0 withr_2.1.2 cli_2.0.2 crayon_1.3.4 readxl_1.3.1 estimability_1.3 evaluate_0.14 fansi_0.4.1 nlme_3.1-144 MASS_7.3-51.5 xml2_1.2.2 foreign_0.8-75 data.table_1.12.6
## [45] hms_0.5.2 lifecycle_0.2.0 munsell_0.5.0 zip_2.0.4 compiler_3.6.3 rlang_0.4.5 grid_3.6.3 nloptr_1.2.1 rstudioapi_0.10 labeling_0.3 rmarkdown_2.1 boot_1.3-24 gtable_0.3.0 abind_1.4-5 curl_4.2 reshape2_1.4.3 R6_2.4.1 lubridate_1.7.4 knitr_1.28 stringi_1.4.6 parallel_3.6.3 Rcpp_1.0.4
## [67] vctrs_0.2.4 tidyselect_1.0.0 xfun_0.12 coda_0.19-3
A work by Haiyang Jin